The subtle art of managing your annoying boss

FORTUNE — Dear Annie: Your column about staying in one’s current job (for now) struck a chord with me, because I too am stuck working for a boss who drives me crazy. I’ve had a couple of other job offers, but I’m only 18 months away from being vested in this company’s defined-benefit pension plan, and — partly because I never stayed anywhere long enough to get vested before — I think it would be smart to stick around at least until then.

The problem is, I report to someone who is a classic example of the Peter Principle — he’s been promoted beyond his ability — and he’s making mistakes that are costing the company money and starting to damage our whole team’s reputation with higher-ups and customers. He also has no sense of boundaries and emails or texts me at all hours of the day and night, and on weekends, over and over again, to ask about things that are not urgent at all. Do you have any suggestions for me? —Counting the Hours

Dear Counting: You probably won’t be surprised to hear that about 75% of people who quit their jobs do so because they can’t stand their bosses, according to a recent Gallup poll of more than a million U.S. employees.

That’s unfortunate, says Jayne Mattson, a senior vice president and executive coach at Boston-based career development firm Keystone Associates, because a little honest communication might go a long way toward fixing at least some of what bugs you. “So many people don’t ever have a candid conversation with their boss about what’s wrong,” she notes. “Instead of trying to make the relationship better, they just leave — and, too often, repeat the same mistake in their next job.”

In short, maybe you need to learn to manage your boss. “There are lots of things you can do to make yourself happier,” says Mattson. “If you manage your boss well, he or she won’t even realize you’re doing it. You’ll just get points for being really helpful.” The key, she explains, is to get what you want by emphasizing how it would benefit him.

First, let’s talk about those incessant texts and emails. About one-third (36%) of employees in a poll last month by consultants Right Management said they work for people who bombard them with emails after regular work hours, and another 15% complained of the same thing on weekends and vacations.

It’s easy to blame technology, and your boss’s lack of boundaries, since both play a part, for sure — but are you unwittingly encouraging these intrusions by answering them right away? “If you respond to every message as soon as you receive it, you’re indicating that you’re available,” says Mattson. “Don’t do that.”

Instead, wait until five or six of them have piled up in your inbox and then respond with a brief message of your own: “I see you have lots of questions about the Ostrich account. Let’s meet first thing tomorrow morning (or Monday morning), when I can give you all the details, and discuss it.” Then stop answering.

“When you do meet, mention that you aren’t always available to reply right away,” Mattson suggests. “Your boss may not even expect you to. Rather than assuming that an immediate answer is required, clarify what it is he actually wants.” There’s always a chance you’ll be pleasantly surprised. Even if not, by declining to answer every time he pings you, you’ll have politely but firmly established the boundaries your boss seems to lack.

Do this now, before you get any more ticked off about it, Mattson adds: “So many people suffer in silence for too long and then blow their stack. But if you have these calm, tactful conversations about relatively minor things, it builds a foundation of trust for when you have to tackle the really tough issues.”

One such issue, clearly: Those costly and reputation-tarnishing errors your boss has been making. “Does he know he’s making these mistakes?” Mattson wonders. “Start by giving him the benefit of the doubt and assuming he’s unaware of the problem.”

Your mission, should you decide to accept it, is to point out what’s going on without blaming anyone in particular. “Describe the errors in terms of the department or the team, and ask whether there’s anything you can do to help prevent any more mistakes,” Mattson says. “Instead of accusing the boss, make it more about the effect on the whole group. Above all, express concern for his reputation, as the leader, if the errors continue, and offer to help develop some possible solutions.”

If this discussion leads nowhere, well, you did what you could. It’s possible, though, that your boss knows things aren’t going well and will react as if you had thrown him a much-needed life preserver — which could be very nice for your own career, too. “If you really make it a priority to build a good rapport with this boss, and help him save face with higher-ups, who knows, you might even decide to stay beyond the next 18 months,” Mattson says. It’s worth a try.

Talkback: Have you ever had a difficult or incompetent boss? How did you deal with him or her? Leave a comment below.